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Search: id:A160406
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| A160406 |
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Toothpick triangle (see Comments lines for definition). |
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+0
21
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| 0, 1, 2, 4, 6, 8, 10, 14, 18, 20, 22, 26, 30, 34, 40, 50, 58, 60, 62, 66, 70, 74, 80, 90, 98, 102, 108, 118, 128, 140, 160, 186, 202, 204, 206, 210, 214, 218, 224, 234, 242, 246, 252, 262, 272, 284, 304, 330, 346, 350, 356, 366, 376, 388, 408, 434, 452, 464, 484, 512, 542, 584
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of toothpick in the sieve after n rounds.
Also, toothpick sequence starting at the corner of an infinite square, but with angle = Pi/4.
The toothpick sequence A139250 is the main entry for this sequence. See also A153000. First differences: A160407.
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FORMULA
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A139250(n) = 2a(n) + 2a(n+1) - 4n - 1 for n>0. - N. J. A. Sloane, May 25 2009
Let G = (x + 2*x^2 + 4*x^2*(1+x)*(mul(1+x^(2^k-1)+2*x^(2^k),k=1..oo)-1)/(1+2*x))/(1-x) (= g.f. for A139250); then the g.f. for the present sequence is (G + 2 + x*(5-x)/(1-x)^2)*x/(2*(1+x)). - N. J. A. Sloane, May 25 2009
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MAPLE
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G := (x + 2*x^2 + 4*x^2*(1+x)*(mul(1+x^(2^k-1)+2*x^(2^k), k=1..20)-1)/(1+2*x))/(1-x); P:=(G + 2 + x*(5-x)/(1-x)^2)*x/(2*(1+x)); series(P, x, 200); seriestolist(%); - N. J. A. Sloane, May 25 2009
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CROSSREFS
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Cf. A139250, A139251, A153000, A153006, A152980, A160407, A160408, A160409.
Sequence in context: A087370 A138929 A151566 this_sequence A113293 A080431 A122642
Adjacent sequences: A160403 A160404 A160405 this_sequence A160407 A160408 A160409
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), May 23 2009
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EXTENSIONS
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More terms from N. J. A. Sloane, May 25 2009
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